Question

Point Q is plotted on the coordinate grid. Point P is at (40, −20). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q?

Answer 1

`\displaystyle d_(RP)=50√(2)\ units`

Explanation:

Distance between points in
`R^2`

If P(p1,p2) and Q(q1,q2) are points on the plane
`R^2`, the distance between them is

`\displaystyle d=√((q_1-p_1)^2+(q_2-p_2)^2)`

We have Q(-10,-20) plotted on the coordinate grid. We also know that P is at (40, -20). We can see they have the same y-coordinate, so the distance between them is computed simply by subtracting their x-coordinates

`\displaystyle d_(PQ)=40-(-10)=50`

We must locate R knowing it's vertically above Q (x-coordinate = -10) and at the same distance from point Q as point P is from point Q. That means that from R to Q there are 50 units. They-coordinate of R will be -20+50=30.

The point R is located at (-10,30)

The distance from R to P is

`\displaystyle d_(RP)=√((-10-40)^2+(30+20)^2)`

`\displaystyle d_(RP)=√((-50)^2+50^2)`

`\displaystyle d_(RP)=√(2500+2500)`

`\displaystyle d_(RP)=√(5000)`

`\displaystyle d_(RP)=50√(2)\ units`